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Scale 475: "Aeolygian"

Scale 475: Aeolygian, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Aeolygian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,7,8}
Forte Number7-Z38
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2929
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 439
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}321.29
G♯{8,0,3}231.57
Minor Triadscm{0,3,7}331.43
c♯m{1,4,8}241.86
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{0,3,6}142.14
c♯°{1,4,7}231.71
Parsimonious Voice Leading Between Common Triads of Scale 475. Created by Ian Ring ©2019 cm cm c°->cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m C+->G# c#°->c#m

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius2
Self-Centeredno
Central VerticesC
Peripheral Verticesc°, c♯m

Modes

Modes are the rotational transformation of this scale. Scale 475 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2285
Scale 2285: Aerogian, Ian Ring Music TheoryAerogian
3rd mode:
Scale 1595
Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
4th mode:
Scale 2845
Scale 2845: Baptian, Ian Ring Music TheoryBaptian
5th mode:
Scale 1735
Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
6th mode:
Scale 2915
Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
7th mode:
Scale 3505
Scale 3505: Stygian, Ian Ring Music TheoryStygian

Prime

The prime form of this scale is Scale 439

Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian

Complement

The heptatonic modal family [475, 2285, 1595, 2845, 1735, 2915, 3505] (Forte: 7-Z38) is the complement of the pentatonic modal family [295, 625, 905, 2195, 3145] (Forte: 5-Z38)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 475 is 2929

Scale 2929Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 475 is chiral, and its enantiomorph is scale 2929

Scale 2929Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian

Transformations:

T0 475  T0I 2929
T1 950  T1I 1763
T2 1900  T2I 3526
T3 3800  T3I 2957
T4 3505  T4I 1819
T5 2915  T5I 3638
T6 1735  T6I 3181
T7 3470  T7I 2267
T8 2845  T8I 439
T9 1595  T9I 878
T10 3190  T10I 1756
T11 2285  T11I 3512

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 473Scale 473: Aeralimic, Ian Ring Music TheoryAeralimic
Scale 477Scale 477: Stacrian, Ian Ring Music TheoryStacrian
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 467Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
Scale 471Scale 471: Dodian, Ian Ring Music TheoryDodian
Scale 459Scale 459: Zaptimic, Ian Ring Music TheoryZaptimic
Scale 491Scale 491: Aeolyrian, Ian Ring Music TheoryAeolyrian
Scale 507Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 219Scale 219: Istrian, Ian Ring Music TheoryIstrian
Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian
Scale 987Scale 987: Aeraptyllic, Ian Ring Music TheoryAeraptyllic
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.